Noether's second theorem for BRST symmetries

TL;DR

This paper extends Noether's second theorem to graded Lagrangian systems with BRST symmetries, accommodating derivatives of variables and ghosts of any order, broadening its applicability in gauge theories.

Contribution

It generalizes Noether's second theorem to include BRST symmetries with derivatives, providing a comprehensive framework for graded Lagrangian systems.

Findings

Proves Noether's second theorem for systems with gauge symmetries depending on derivatives.

Extends the theorem to graded Lagrangian systems with even and odd variables.

Provides foundational results for BRST symmetry analysis in advanced gauge theories.

Abstract

We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether's second theorem for Lagrangian systems on fiber bundles over X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved.